def pearson_correlation(X, Y):
"""
Considering the rows of X (and Y=X) as vectors, compute the
distance matrix between each pair of vectors.
This correlation implementation is equivalent to the cosine similarity
since the data it receives is assumed to be centered -- mean is 0. The
correlation may be interpreted as the cosine of the angle between the two
vectors defined by the users' preference values.
Parameters
----------
X : {array-like, sparse matrix}, shape = [n_samples_1, n_features]
Y : {array-like, sparse matrix}, shape = [n_samples_2, n_features]
Returns
-------
distances : {array, sparse matrix}, shape = [n_samples_1, n_samples_2]
Examples
--------
>>> from crab.metrics.pairwise import pearson_correlation
>>> X = [[2.5, 3.5, 3.0, 3.5, 2.5, 3.0],[2.5, 3.5, 3.0, 3.5, 2.5, 3.0]]
>>> # distance between rows of X
>>> pearson_correlation(X, X)
array([[ 1., 1.],
[ 1., 1.]])
>>> pearson_correlation(X, [[3.0, 3.5, 1.5, 5.0, 3.5,3.0]])
array([[ 0.39605902],
[ 0.39605902]])
"""
# should not need X_norm_squared because if you could precompute that as
# well as Y, then you should just pre-compute the output and not even
# call this function.
from distmetrics import DistanceMetric
X, Y = check_pairwise_arrays(X, Y)
n_samples_X, n_features_X = X.shape
n_samples_Y, n_features_Y = Y.shape
if n_features_X != n_features_Y:
raise Exception("X and Y should have the same number of features!")
if X is Y:
X = Y = np.asanyarray(X)
else:
X = np.asanyarray(X)
Y = np.asanyarray(Y)
dm = DistanceMetric(metric='correlation')
D = dm.pdist(X, squareform=True)
return 1 - D
def bench_float(m1=200, m2=200, rseed=0):
print 79 * '_'
print " real valued distance metrics"
print
np.random.seed(rseed)
X1 = np.random.random((m1, DTEST))
X2 = np.random.random((m2, DTEST))
for (metric, argdict) in METRIC_DICT.iteritems():
keys = argdict.keys()
for vals in itertools.product(*argdict.values()):
kwargs = dict(zip(keys, vals))
print metric, param_info(kwargs)
t0 = time()
try:
dist_metric = DistanceMetric(metric, **kwargs)
Yc1 = dist_metric.cdist(X1, X2)
except Exception as inst:
print " >>>>>>>>>> error in pyDistances cdist:"
print " ", inst
t1 = time()
try:
Yc2 = cdist(X1, X2, metric, **kwargs)
except Exception as inst:
print " >>>>>>>>>> error in scipy cdist:"
print " ", inst
t2 = time()
try:
dist_metric = DistanceMetric(metric, **kwargs)
Yp1 = dist_metric.pdist(X1)
except Exception as inst:
print " >>>>>>>>>> error in pyDistances pdist:"
print " ", inst
t3 = time()
try:
Yp2 = pdist(X1, metric, **kwargs)
except Exception as inst:
print " >>>>>>>>>> error in scipy pdist:"
print " ", inst
t4 = time()
if not np.allclose(Yc1, Yc2):
print " >>>>>>>>>> FAIL: cdist results don't match"
if not np.allclose(Yp1, Yp2):
print " >>>>>>>>>> FAIL: pdist results don't match"
print " - pyDistances: c: %.4f sec p: %.4f sec" % (t1 - t0,
t3 - t2)
print " - scipy: c: %.4f sec p: %.4f sec" % (t2 - t1,
t4 - t3)
print ''
def bench_float(m1=100, m2=100, rseed=0):
print 79 * '_'
print " real valued distance metrics"
print
np.random.seed(rseed)
X1 = np.random.random((m1, DTEST))
X2 = np.random.random((m2, DTEST))
for (metric, argdict) in METRIC_DICT.iteritems():
keys = argdict.keys()
for vals in itertools.product(*argdict.values()):
kwargs = dict(zip(keys, vals))
print metric, param_info(kwargs)
t0 = time()
try:
dist_metric = DistanceMetric(metric, **kwargs)
Yc1 = dist_metric.cdist(X1, X2)
except Exception as inst:
print " >>>>>>>>>> error in pyDistances cdist:"
print " ", inst
t1 = time()
try:
Yc2 = cdist(X1, X2, metric, **kwargs)
except Exception as inst:
print " >>>>>>>>>> error in scipy cdist:"
print " ", inst
t2 = time()
try:
dist_metric = DistanceMetric(metric, **kwargs)
Yp1 = dist_metric.pdist(X1)
except Exception as inst:
print " >>>>>>>>>> error in pyDistances pdist:"
print " ", inst
t3 = time()
try:
Yp2 = pdist(X1, metric, **kwargs)
except Exception as inst:
print " >>>>>>>>>> error in scipy pdist:"
print " ", inst
t4 = time()
if not np.allclose(Yc1, Yc2):
print " >>>>>>>>>> FAIL: cdist results don't match"
if not np.allclose(Yp1, Yp2):
print " >>>>>>>>>> FAIL: pdist results don't match"
print " - pyDistances: c: %.2g sec p: %.2g sec" % (t1 - t0,
t3 - t2)
print " - scipy: c: %.2g sec p: %.2g sec" % (t2 - t1,
t4 - t3)
print ''
def test_ball_tree_query_radius_count(n_samples=100, n_features=10):
X = 2 * np.random.random(size=(n_samples, n_features)) - 1
dm = DistanceMetric()
D = dm.pdist(X, squareform=True)
r = np.mean(D)
bt = BallTree(X)
count1 = bt.query_radius(X, r, count_only=True)
count2 = (D <= r).sum(1)
assert_array_almost_equal(count1, count2)
def _check_metrics_float(self, k, metric, kwargs):
bt = BallTree(self.X, metric=metric, **kwargs)
dist_bt, ind_bt = bt.query(self.X, k=k)
dm = DistanceMetric(metric=metric, **kwargs)
D = dm.pdist(self.X, squareform=True)
ind_dm = np.argsort(D, 1)[:, :k]
dist_dm = D[np.arange(self.X.shape[0])[:, None], ind_dm]
# we don't check the indices here because if there is a tie for
# nearest neighbor, then the test may fail. Distances will reflect
# whether the search was successful
assert_array_almost_equal(dist_bt, dist_dm)
def test_ball_tree_query_radius_count(n_samples=100, n_features=10):
X = 2 * np.random.random(size=(n_samples, n_features)) - 1
dm = DistanceMetric()
D = dm.pdist(X, squareform=True)
r = np.mean(D)
bt = BallTree(X)
count1 = bt.query_radius(X, r, count_only=True)
count2 = (D <= r).sum(1)
assert_array_almost_equal(count1, count2)
def _check_metrics_float(self, k, metric, kwargs):
bt = BallTree(self.X, metric=metric, **kwargs)
dist_bt, ind_bt = bt.query(self.X, k=k)
dm = DistanceMetric(metric=metric, **kwargs)
D = dm.pdist(self.X, squareform=True)
ind_dm = np.argsort(D, 1)[:, :k]
dist_dm = D[np.arange(self.X.shape[0])[:, None], ind_dm]
# we don't check the indices here because if there is a tie for
# nearest neighbor, then the test may fail. Distances will reflect
# whether the search was successful
assert_array_almost_equal(dist_bt, dist_dm)
def test_query_radius_count(self):
# center the data
X = 2 * self.X - 1
dm = DistanceMetric()
D = dm.pdist(X, squareform=True)
r = np.mean(D)
bt = BallTree(X)
count1 = bt.query_radius(X, r, count_only=True)
count2 = (D <= r).sum(1)
assert_array_almost_equal(count1, count2)
def test_query_radius_count(self):
# center the data
X = 2 * self.X - 1
dm = DistanceMetric()
D = dm.pdist(X, squareform=True)
r = np.mean(D)
bt = BallTree(X)
count1 = bt.query_radius(X, r, count_only=True)
count2 = (D <= r).sum(1)
assert_array_almost_equal(count1, count2)
def test_pdist(m=15, rseed=0):
"""Compare DistanceMetric.pdist to scipy.spatial.distance.pdist"""
np.random.seed(rseed)
X = np.random.random((m, DTEST))
for (metric, argdict) in METRIC_DICT.iteritems():
keys = argdict.keys()
for vals in itertools.product(*argdict.values()):
kwargs = dict(zip(keys, vals))
dist_metric = DistanceMetric(metric, **kwargs)
Y1 = dist_metric.pdist(X)
Y2 = pdist(X, metric, **kwargs)
if not np.allclose(Y1, Y2):
print metric, keys, vals
print Y1[:5, :5]
print Y2[:5, :5]
assert np.allclose(Y1, Y2)
def test_pdist(m=15, rseed=0):
"""Compare DistanceMetric.pdist to scipy.spatial.distance.pdist"""
np.random.seed(rseed)
X = np.random.random((m, DTEST))
for (metric, argdict) in METRIC_DICT.iteritems():
keys = argdict.keys()
for vals in itertools.product(*argdict.values()):
kwargs = dict(zip(keys, vals))
dist_metric = DistanceMetric(metric, **kwargs)
Y1 = dist_metric.pdist(X)
Y2 = squareform(pdist(X, metric, **kwargs))
if not np.allclose(Y1, Y2):
print metric, keys, vals
print Y1[:5, :5]
print Y2[:5, :5]
assert np.allclose(Y1, Y2)
def test_pdist_squareform(m=10, d=3, rseed=0):
X = np.random.random((m, d))
dist_metric = DistanceMetric()
Y1 = squareform(dist_metric.pdist(X, squareform=False))
Y2 = dist_metric.pdist(X, squareform=True)
assert np.allclose(Y1, Y2)
def test_pdist_squareform(m=10, d=3, rseed=0):
X = np.random.random((m, d))
dist_metric = DistanceMetric()
Y1 = squareform(dist_metric.pdist(X, squareform=False))
Y2 = dist_metric.pdist(X, squareform=True)
assert np.allclose(Y1, Y2)
